For the impatient, here is the code, which also contains my final report.


This is probably long overdue, but I really want to write about my masters project while it is still fresh on my mind (masters thesis, dissertation, or final year project report, whatever you want to call it. I would like to call it a thesis since it sounds loads cooler than the rest, but unfortunately my school just calls it the project report). It was submitted some time ago, and it is something I am quite proud of.

It didn't really start on a good note: the project was supposed to be done in pairs (though all assessments are separate) but my partner couldn't come back for fourth year due to personal reasons, and I had to do it alone. I sent a frantic email to my supervisor, and he told me that there is no problem doing this project alone. Though, it was also him who said that to get started with this project, "you just need to learn a little bit of General Relativity, shouldn't be too difficult."

He also mentioned that two other people (a PhD student and a postdoc) have previously attempted this project, but both ran out of time before they could finish it. So I was not particularly optimistic.

But it did end well. Here are the excerpts of the continuous assessment comments from my supervisor:

Lingyi has done an outstanding job with this project, showing great initiative in researching the literature very well, finding more than one relevant paper that I was not aware of. The results may be publishable in a journal paper, dependent on a period of digestion and the acquisition of understanding of what they mean, since there are a number of subtleties to comprehend. She has shown a great deal of independence, critical thinking, and self-motivation, looking at new ways of tackling the problem, and requiring only a small amount of guidance, and has worked hard.

and some comments on the viva:

Lingyi has read all of the literature that I am aware of, and some I was not, but here in the talk she concentrated on a few key papers, and she chose exactly the right ones.

Lingyi answered the questions with complete authority. She has clearly mastered her topic, and all the answers were correct.

I'm quite pleased, to say the least.

So, what was it about? There have been some previous posts that spun off my final year project (see Distances in Schwarzschild lensing and Numerical integration of light paths in a Schwarzschild metric) that might give you an idea. The one line summary is this: we want to know if the cosmological constant affects gravitational lensing.

This question basically splits the research into two camps: one believes yes, the other believes no. My supervisor is in the "no" camp.

Of course this statement is not entirely accurate and it is more complicated than that, such as the fact that gravitational lensing in a cosmological context depends on angular diameter distance which already has a dependence on the cosmological constant, so the real question is whether the current formula is enough, and also that angle and distance measurements are not always clearly defined when space is not asymptotically flat, so we have to clearly state what we refer to when we say "bending angle". But regardless, this is the essential question. Surprisingly, given how widely used gravitational lensing is and how widely accepted the cosmological constant is, there is not yet a consensus on this. We hope to answer the question numerically instead of analytically.

Anyway, this post was not meant to be a full description of what my project is—I have my report for that. If you're curious, our answer to whether the cosmological constant affects gravitational lensing is, as with most research questions: maybe. More specifically, due to the intricacies of our cosmological model, it is difficult to truly isolate the effect of the cosmological constant on lensing.

I briefly considered putting a graph of my results here, but I think it is rather irresponsible to post a results graph without explaining its intricacies and nuanced implications, and it is difficult to do that in a single blog post without an exposition of the background literature.

There is no doubt that I loved the journey, though there were multiple stressul points along the way. It has always been my dream to do astronomy-related research and I can't thank my supervisor Alan Heavens enough for proposing this project that is at the same time both challenging and not undoable. The project answers a real research question and the process of doing it makes me feel like I am genuinely contributing to the pool of collective scientific knowledge.

Of couse, self-doubt was frequent and imposter syndrome plagued me along the way...

PHD Comics: Imposter, Pt. 4
"Imposter" - created by PHD Comics

But I did it! It was an amazing feeling that nearer the second half of my project, I could understand most of the research papers that I struggled with initially, and more than that, I also understood some of their problems. It's sad that perhaps this is my last contact with true physics research for a long time (or likely for good), and this project was important enough in my life that it deserves a formal goodbye.